Formula:10306

Digital Library of Mathematical Functions ID 33.14.E5

${\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=(2r)^{\ell+1}e^{-r/\kappa}M\left(\ell+1-\kappa,2\ell+2,2r/\kappa\right)/{(2\ell+1)!},}}$

Symbols List

• ${\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)}}$: regular Coulomb function
• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle r}}$: real variable
• ${\displaystyle{\displaystyle\epsilon}}$: real parameter
• ${\displaystyle{\displaystyle\kappa}}$: quantity (locally)
 

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